1) No solution AT ALL, certainly would be "No Unique Solution"
2) More than one solution also would be "No Unique Solution"

#1 is trivial: 3*a - (5)*(-2) = 3a + 10 = 0 ==> a = -10/3
Another way to do this would be to put both linear equations into Slope-Intercept form. Setting the slopes equal and solving for 'a' gives the desired result. If the slopes are equal, the lines must be parallel and there is no common solution, unless...

#2 is a bit trickier, since we must show the two linear equations to represent exactly the same line. Unfortunately, we have a Degrees of Freedom problem. We can make EITHER the slopes equal OR the y-intercepts equal. We can't do both simultaneously.

1) No solution AT ALL, certainly would be "No Unique Solution"
2) More than one solution also would be "No Unique Solution"

#1 is trivial: 3*a - (5)*(-2) = 3a + 10 = 0 ==> a = -10/3
Another way to do this would be to put both linear equations into Slope-Intercept form. Setting the slopes equal and solving for 'a' gives the desired result. If the slopes are equal, the lines must be parallel and there is no common solution, unless...

#2 is a bit trickier, since we must show the two linear equations to represent exactly the same line. Unfortunately, we have a Degrees of Freedom problem. We can make EITHER the slopes equal OR the y-intercepts equal. We can't do both simultaneously.

No, this can't happen. If we multiply the second equation by , we have and
There is NO value of a which will make the second equation the same as the first.